To study means to try to learn. It means that you read, think, talk and write about the subject you are trying to understand. Studying usually implies something that happens over a long period of time, for example, taking a 3 year course in English means you are studying English.
To learn means that you understand something. It is the end-product of studying. Learning something is usually a short process - once you have learnt it, you don't need to study it anymore.